Dayton, October 16, 1901
Your letters with enclosures rec'd. I thank you very much for Lilienthal's Plate VII. The Obermayer article I will return as soon as I have time to read it more carefully. I think he is right in saying that Lilienthal should have taken account of the position of the center of pressure, which according to Obermayer he did not do. I was not previously aware that Lilienthal had made tables for both natural wind and still air, the former being about 50 percent greater than the latter. I was also interested in your statement that the .005 coefficient was that of experimenters in natural wind and .003 that of still air. Now if the regular Lilienthal table is that of natural wind, and .13 metric that of natural wind also, is it not a little inconsistent in Lilienthal and Herring to claim performances in still air slightly exceeding that calculated from the values for natural wind, whereas if the still air values had been used, the performance would have been double that calculated as possible? It would seem that still air is really as effective as natural wind in actual practice, and I can see no theoretical reason why it should not be. I admit that the sum of the square of two numbers is greater than the square of their mean and that therefore a fluctuating wind is more effective than a uniform one, but the tables are based on ratio of Pa to P90, and the fluctuation has just as much effect on the normal as on the inclined surface, so that the ratio remains constant; and the same fluctuations which increase the lift on inclined surfaces will likewise cause the anemometer to overrecord the real velocity, so that I can see no theoretical reason why the values in still air should be different from those in the natural wind. On the other hand I see several good reasons why measurements made in natural wind should seem to give higher values. First. The wind gusts come on suddenly with great power and then die gradually away. The result is that the instrument is moved from the lowest to the highest point with a speed which causes its momentum to carry it far beyond the correct position for the highest pressure, while on the ebb the instrument moves so slowly that it does not appreciably underrecord the lowest pressure. The result is that the apparent average is too high. Second. The gusts are of short duration as compared with the slower velocities. Consequently the mean of the highest and lowest pressures is not the average of the work actually performed. Third. In measurements in the open air it is impossible to determine the actual angle of incidence within several degrees, and as measurements are usually made during a gust, at which time the wind usually has a slight upward trend, the measurement taken may be that of a greater angle than supposed. Fourth. The wind velocity in outdoor tests where the pressures are measured by springs must be taken with an anemometer, which must occupy a different position from that of the surface whose pressure is being measured, and which may itself not record velocities truly. Nevertheless, though theory seems to us to indicate that still air or air from a fan is as effective in proportion on an inclined surface as on a normal one, we shall test natural wind also.
Since beginning this letter I have read the Obermayer article more carefully and fully agree with him that the position of the center of pressure must be considered in determining the tangential with an instrument such as he represents Lilienthal as using.
This can be clearly shown by using a plane surface on which pressures cannot be other than normal. If a wind vane turning on the axis c have the blade mounted perpendicular to the arm ca, instead of parallel as in the usual style of vanes, it will nevertheless take up the position ca although in theory it ought to stand at any angle at which it is placed, for instance ca', for the pressure being in the direction ca' there would be nothing to move it either to right or left. But in fact the pressure being applied at x in the direction yx pushes the vane back to ca or until the line yx coincides with ca'. Thus it is evident that a pressure perpendicular to the chord of a curved surface would likewise give it an apparent tangential pressure if the center of pressure be in front or behind the point to which the arm ca is perpendicular. However, even if Lilienthal really made a mistake in his apparatus for measurement, the tangential may still exist, and this Obermayer seems to have found.
The instrument with which we expect to measure the lifts and drifts of variously shaped surfaces is on the principle shown in the diagram. On the vertical axles cc' are fastened the horizontal arms x and x' which bear a crosspiece a on which a normal plane is mounted. The horizontal arms y and y' are equal in length to x and x', and are mounted on friction sleeves which fit the axles c & c'. They bear the crosspiece on which the surface to be tested is mounted. This method of mounting the surface preserves its exact angle of incidence regardless of the angular position of the arms y and y', and also renders it indifferent where the center of pressure is located.
In use, the surface is mounted on the crossarm at any desired angle, and the wind turned on. The "lift" moves the arms yy' to the right and the arms xx' which bear the normal plane to the left. The arms yy' which have a friction mounting on the axles cc' are moved back to zero and readjusted till they remain there. The angle of the arms xx' is indicated by the stationary protractor. The sine of the angle zcx is the lift of the surface, for the angle at which it is set, in percent of P9O. The wind from the fan is rendered uniform in direction by the same means which Prof. Marey employed so successfully in the photographs you showed us at Kitty Hawk. In velocity the wind consists of a rapid succession of pulsations. The speed we have not measured but is probably about 40 ft. per second. At present we find that the position of the normal plane produces a slight change in the direction of the wind which strikes the inclined surface, and that the inclined surface slightly affects the velocity of the wind on the normal surface. We find that these errors are very slight, amounting to probably less than 10 percent. In a new instrument we hope to avoid them entirely. In experiments in the open we find that the position of the operator, even if several feet to leeward of the instrument, seriously affects the results, according to whether he stands to right or left. We have accordingly mounted the instrument in a long box or trough, with a glass cover, so that now successive observations at a given angle give the same results. The chart enclosed is subject to errors of perhaps ten percent. I send it as indicating the direction of our results rather than as exact values. The latter we hope to get within a very few percent of perfection with our improved instrument. You will note that the lift of square planes at small angles is but little more than one half that of Langley's "corrected curve," while the same surfaces with end plates to keep the wind from slipping off, and which therefore correspond to surfaces of infinite breadth, are very close to the Duchemin formula. As Langley used no end plates on his square surfaces the question rises whether he did not draw his "corrected curve" after seeing the Duchemin tables to which it corresponds.
The negative angles at which curved surfaces begin to lift are within 1/4 of a degree of absolute truth, I think. You will note that the square surfaces begin lifting at a greater negative angle than the wide surfaces or the surfaces with end plates. The Plin's curve at 5° is only about .66 as effective as a regular curve or a parabola when placed in the usual position, but when turned with the curve backward is almost their equal. The heavy black line shows a Lilienthal curve 3" X 3" with end plates. A similarly curved surface 1.5" X 6" gives almost equal results. This line compares quite closely with Lilienthal's curve for still air.
It would appear that Lilienthal is very much nearer the truth than we have heretofore been disposed to think. However, we think he is in error in using 0.13, so that altogether his estimate of the lift of his machine at 9 meters is about double what seems reasonable to us. Using the Plin's curve line and .0033 per mile we get results corresponding very well with our Kitty Hawk observations.
I am inclined to think that the value for P90 obtained by the Weather Bureau as given in the pamphlet on Anemometry is the best yet obtained. It was made in natural wind by the use of pressure plates recording on a cylinder. Their estimate varies from .0035 to .0025 at speeds from 20 miles to 40 miles indicated velocity; and .004 for corrected velocities at all speeds. As we found the Richard's instrument to correspond reasonably closely with the Robinson, which is 10 percent too high at 20 miles per hour, it is evident that in our observations at least the value .0033 should be used for indicated speeds from 18 to 22 miles per hour.
Do you know what anemometer Lilienthal used, or in what wind velocity his observations were made? At low speeds the Robinson and Richard's underrecord the true velocities, while at high speeds the reverse is true. In our experiments we simultaneously expose both the inclined surface and the normal plane to the same wind, and the results are the same regardless of changes in the wind speed.
You will remember that the chart enclosed is for lift only. We will also measure the drift later. We are inclined to think that the drift of deeply curved surfaces (1/12) will be somewhat greater at small angles than Lilienthal's tangential added to the horizontal component would indicate, though we have made no close measurements yet.
This chart is from a single series of observations at 0°, 2.5°, 5°, 7.5°, & 10°. It is not an average of a series of measurements. The curves are not "corrected." It is from observations with our first machine which is not believed to give exact results except at .000, or the point at which lift begins. The other values are probably too high by about the amount by which line 3 exceeds Duchemin.
Lilienthal's curve with the quicker curve to the rear gives slightly greater results than in the regular position. A plain curve fully equals the Lilienthal curve.
We have tried a number of forms intermediate between Plin's and the plain curve, both forward and backward, and are inclined to think that -4.5° is about the limit of negative angle for wide narrow surfaces or surfaces with ends. With surfaces having greater longitudinal than lateral dimensions a slightly greater negative angle can be obtained, the greatest so far being -7°.